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Galaxy cluster number count has been proven to be a powerful cosmological probe. However, cosmological constraints established with galaxy cluster number count are highly dependent on the calibration of the mass-observable relations. Thanks to its nearly mass independence the specific mass accretion rate of galaxy clusters is nearly insensitive to the calibration of mass-observable relations. The study of galaxy cluster number count evolution allows to probe the galaxy cluster mass accretion history in the context of an homogenous Universe. In this paper, we use relative abundance matching to infer the galaxy cluster mass accretion rate (MAR) for $z in [0.0,0.6[$. Then, we use the MAR to set cosmological constraints. We found that this cosmological probe is sensitive to $sigma_8 Omega_{rm m}^{-0.3} H_0^{-0.2}$ whereas the galaxy cluster count is sensitive to $sigma_8 Omega_{rm m}^{0.3}$. We used the second $Planck$ catalog of Sunyaev-Zeldovich sources and we derive $sigma_8 Omega_{rm m}^{-0.3} H_0^{-0.2} = 0.75 pm 0.06$. This results is consistent with cosmological constraints derived from galaxy clusters number counts, angular power spectrum, and cosmic microwave background analyses. Therefore, the MAR is a key cosmological probe that can break the $sigma_8$-$Omega_{rm m}$ degeneracy and that is not sensitive to the calibration of the mass-observable relations and does not requires a parametric form for the galaxy cluster mass-function.
The total mass of a galaxy cluster is one of its most fundamental properties. Together with the redshift, the mass links observation and theory, allowing us to use the cluster population to test models of structure formation and to constrain cosmolog
We present the cosmological parameters constraints obtained from the combination of galaxy cluster mass function measurements (Vikhlinin et al., 2009a,b) with new cosmological data obtained during last three years: updated measurements of cosmic micr
The halo mass function (HMF) is a critical element in cosmological analyses of galaxy cluster catalogs. We quantify the impact of uncertainties in HMF parameters on cosmological constraints from cluster catalogs similar to those from Planck, those ex
In recent years, the availability of large, complete cluster samples has enabled numerous cosmological parameter inference analyses using cluster number counts. These have provided constraints on the cosmic matter density $Omega_m$ and the amplitude
Sunyaev-Zeldovich (SZ) surveys are promising probes of cosmology - in particular for Dark Energy (DE) -, given their ability to find distant clusters and provide estimates for their mass. However, current SZ catalogs contain tens to hundreds of objec